The Optimization–Fragility Paradox: Slack Vectors, Novelty, and Cascading Risk in Heavy-Tailed Environments

Complex systems, whether evolved or engineered, frequently exhibit a "robust-yet-fragile" (RYF) architecture: they are robust to anticipated perturbations but hypersensitive to rare, unanticipated events. This phenomenon is formalized within the Highly Optimized Tolerance (HOT) framework. This paper proposes the "Optimization-Fragility Paradox" as an operational unification of these concepts. We argue that optimization tends to maximize resource utilization by minimizing general-purpose physical and temporal slack, effectively transferring the burden of resilience to informational/control slack. When novelty (out-of-distribution conditions) degrades the generalization capability of control mechanisms, the probability of cascading failure increases non-linearly, particularly in environments characterized by heavy-tailed disturbance statistics. We introduce a formal model utilizing a Slack Vector, a continuous novelty parameter, and a hazard–survival formulation for Probability of Ruin, ensuring that failure probabilities remain bounded and estimable from time-to-event data. This framework is applied to: (i) the diffusion–barrier trade-off (Fick’s Law) in biophysics, (ii) the hormetic dose–response model to ethically frame psychosocial resilience, and (iii) tightly coupled just-in-time supply chins.